NYC taxi

Python
Pandas
Numpy
Scipy
Author

Hyunsoo Kim

Published

May 24, 2022

NYC taxi

Visual Analytics with Python

강의자료 출처 - kaggle.com

In this script we will explore the spatial and temporal behavior of the people of New York as can be inferred by examining their cab usage.

The main fields of this dataset are taxi pickup time and location, as well as dropoff location and trip duration. There is a total of around 1.4 Million trips in the dataset that took place during the first half of 2016.

We will study how the patterns of cab usage change throughout the year, throughout the week and throughout the day, and we will focus on difference between weekdays and weekends.

%matplotlib inline

from sklearn import decomposition
from scipy import stats
from sklearn import cluster
import numpy as np
import pandas as pd
import matplotlib
import matplotlib.pyplot as plt

matplotlib.style.use('fivethirtyeight')
matplotlib.rcParams['font.size'] = 12
matplotlib.rcParams['figure.figsize'] = (10,10)

Load data and preprocess measurements to sensible units

data_frame = pd.read_csv('train.csv')
data_frame.describe()
vendor_id passenger_count pickup_longitude pickup_latitude dropoff_longitude dropoff_latitude trip_duration
count 1.458644e+06 1.458644e+06 1.458644e+06 1.458644e+06 1.458644e+06 1.458644e+06 1.458644e+06
mean 1.534950e+00 1.664530e+00 -7.397349e+01 4.075092e+01 -7.397342e+01 4.075180e+01 9.594923e+02
std 4.987772e-01 1.314242e+00 7.090186e-02 3.288119e-02 7.064327e-02 3.589056e-02 5.237432e+03
min 1.000000e+00 0.000000e+00 -1.219333e+02 3.435970e+01 -1.219333e+02 3.218114e+01 1.000000e+00
25% 1.000000e+00 1.000000e+00 -7.399187e+01 4.073735e+01 -7.399133e+01 4.073588e+01 3.970000e+02
50% 2.000000e+00 1.000000e+00 -7.398174e+01 4.075410e+01 -7.397975e+01 4.075452e+01 6.620000e+02
75% 2.000000e+00 2.000000e+00 -7.396733e+01 4.076836e+01 -7.396301e+01 4.076981e+01 1.075000e+03
max 2.000000e+00 9.000000e+00 -6.133553e+01 5.188108e+01 -6.133553e+01 4.392103e+01 3.526282e+06 
data_frame.shape
(1458644, 11)
np.max(data_frame['trip_duration']) #이렇게 보면서 이상치가 있는 것을 눈으로 봄 3526282(전처리전) --> 4764(전처리후)
3526282
# remove obvious outliers / 위경도 좌표가 튀는 것을 제거 
allLat  = np.array(list(data_frame['pickup_latitude'])  + list(data_frame['dropoff_latitude'])) #두개의 컬럼을 리스트로 합쳐줌 
allLong = np.array(list(data_frame['pickup_longitude']) + list(data_frame['dropoff_longitude']))

longLimits = [np.percentile(allLong, 0.3), np.percentile(allLong, 99.7)]
latLimits  = [np.percentile(allLat , 0.3), np.percentile(allLat , 99.7)]
durLimits  = [np.percentile(data_frame['trip_duration'], 0.4), np.percentile(data_frame['trip_duration'], 99.7)]

data_frame = data_frame[(data_frame['pickup_latitude']   >= latLimits[0] ) & (data_frame['pickup_latitude']   <= latLimits[1]) ] #이상치 제거
data_frame = data_frame[(data_frame['dropoff_latitude']  >= latLimits[0] ) & (data_frame['dropoff_latitude']  <= latLimits[1]) ]
data_frame = data_frame[(data_frame['pickup_longitude']  >= longLimits[0]) & (data_frame['pickup_longitude']  <= longLimits[1])]
data_frame = data_frame[(data_frame['dropoff_longitude'] >= longLimits[0]) & (data_frame['dropoff_longitude'] <= longLimits[1])]
data_frame = data_frame[(data_frame['trip_duration']     >= durLimits[0] ) & (data_frame['trip_duration']     <= durLimits[1]) ]
data_frame = data_frame.reset_index(drop=True)
# convert fields to sensible units
medianLat  = np.percentile(allLat,50)
medianLong = np.percentile(allLong,50)

latMultiplier  = 111.32
longMultiplier = np.cos(medianLat*(np.pi/180.0)) * 111.32

data_frame['duration [min]'] = data_frame['trip_duration']/60.0
data_frame['src lat [km]']   = latMultiplier  * (data_frame['pickup_latitude']   - medianLat)
data_frame['src long [km]']  = longMultiplier * (data_frame['pickup_longitude']  - medianLong)
data_frame['dst lat [km]']   = latMultiplier  * (data_frame['dropoff_latitude']  - medianLat)
data_frame['dst long [km]']  = longMultiplier * (data_frame['dropoff_longitude'] - medianLong)

allLat  = np.array(list(data_frame['src lat [km]'])  + list(data_frame['dst lat [km]']))
allLong = np.array(list(data_frame['src long [km]']) + list(data_frame['dst long [km]']))

Plot the histograms of trip duration, latitude and longitude

fig, axArray = plt.subplots(nrows=1,ncols=3,figsize=(13,4))
axArray[0].hist(data_frame['duration [min]'],80);
axArray[0].set_xlabel('trip duration [min]'); axArray[0].set_ylabel('counts')
axArray[1].hist(allLat ,80); axArray[1].set_xlabel('latitude [km]')
axArray[2].hist(allLong,80); axArray[2].set_xlabel('longitude [km]')
#위경도는 큰의미는 없지만 플랏으로 이상치가 있는지 시각적으로 확인 
Text(0.5, 0, 'longitude [km]')

Plot the trip Duration vs. the Aerial Distance between pickup and dropoff

data_frame['log duration']       = np.log1p(data_frame['duration [min]'])
data_frame['euclidian distance'] = np.sqrt((data_frame['src lat [km]']  - data_frame['dst lat [km]'] )**2 +
                                       (data_frame['src long [km]'] - data_frame['dst long [km]'])**2)

fig, axArray = plt.subplots(nrows=1,ncols=2,figsize=(13,6))
axArray[0].scatter(data_frame['euclidian distance'], data_frame['duration [min]'],c='b',s=5,alpha=0.01);
axArray[0].set_xlabel('Aerial Euclidian Distance [km]'); axArray[0].set_ylabel('Duration [min]')
axArray[0].set_xlim(data_frame['euclidian distance'].min(),data_frame['euclidian distance'].max())
axArray[0].set_ylim(data_frame['duration [min]'].min(),data_frame['duration [min]'].max())
axArray[0].set_title('trip Duration vs Aerial trip Distance')

axArray[1].scatter(data_frame['euclidian distance'], data_frame['log duration'],c='b',s=5,alpha=0.01);
axArray[1].set_xlabel('Aerial Euclidian Distance [km]'); axArray[1].set_ylabel('log(1+Duration) [log(min)]')
axArray[1].set_xlim(data_frame['euclidian distance'].min(),data_frame['euclidian distance'].max())
axArray[1].set_ylim(data_frame['log duration'].min(),data_frame['log duration'].max())
axArray[1].set_title('log of trip Duration vs Aerial trip Distance')
Text(0.5, 1.0, 'log of trip Duration vs Aerial trip Distance')

Exercise 1

위의 Scatter plot은 Point가 너무 많이 존재하여 좋은 시각화가 아닐 수 있습니다. 보다 효율적인 시각화 방안을 제시해 보세요.

matplotlib, seaborn, plotly 등 다양한 패키지를 활용할 수 있습니다

import seaborn as sns

sns.jointplot(x=data_frame['euclidian distance'], 
              y=data_frame['duration [min]'], 
              kind="hex", 
              color="#4CB391",
              xlim = (0,30),
              ylim = (0,70))

p = sns.jointplot(x=np.log1p(data_frame['euclidian distance']),
              y=data_frame['log duration'], 
              kind="hex", 
              color="#4CB391") #log를 취해 주어서 히트맵을 변환시켜 보여줌 

p.ax_joint.set_xlabel('log(1+Aerial Euclidian Distance) [log(km)]')
p.ax_joint.set_ylabel('log(1+Duration) [log(min)]')
Text(8.060000000000002, 0.5, 'log(1+Duration) [log(min)]')

We can see that the trip distance defines the lower bound on trip duration, as one would expect.

Plot spatial density plot of the pickup and dropoff locations

imageSize = (700,700)
longRange = [-5,19]
latRange = [-13,11]

allLatInds  = imageSize[0] - (imageSize[0] * (allLat  - latRange[0])  / (latRange[1]  - latRange[0]) ).astype(int)
allLongInds =                (imageSize[1] * (allLong - longRange[0]) / (longRange[1] - longRange[0])).astype(int)

locationDensityImage = np.zeros(imageSize)
for latInd, longInd in zip(allLatInds,allLongInds):
    locationDensityImage[latInd,longInd] += 1

fig, ax = plt.subplots(nrows=1,ncols=1,figsize=(12,12))
ax.imshow(np.log(locationDensityImage+1),cmap='inferno')
ax.set_axis_off()

Exercise 2

folium이나 pydeck을 사용하여 택시의 승차지점, 하차지점을 시각화 해봅시다. 디서 승객이 많이 타고 내리는지를 확인할 수 있습니까?

data_frame.head()
id vendor_id pickup_datetime dropoff_datetime passenger_count pickup_longitude pickup_latitude dropoff_longitude dropoff_latitude store_and_fwd_flag trip_duration duration [min] src lat [km] src long [km] dst lat [km] dst long [km] log duration euclidian distance
0 id2875421 2 2016-03-14 17:24:55 2016-03-14 17:32:30 1 -73.982155 40.767937 -73.964630 40.765602 N 455 7.583333 1.516008 -0.110015 1.256121 1.367786 2.149822 1.500479
1 id2377394 1 2016-06-12 00:43:35 2016-06-12 00:54:38 1 -73.980415 40.738564 -73.999481 40.731152 N 663 11.050000 -1.753813 0.036672 -2.578912 -1.571088 2.489065 1.807119
2 id3858529 2 2016-01-19 11:35:24 2016-01-19 12:10:48 1 -73.979027 40.763939 -74.005333 40.710087 N 2124 35.400000 1.070973 0.153763 -4.923841 -2.064547 3.594569 6.392080
3 id3504673 2 2016-04-06 19:32:31 2016-04-06 19:39:40 1 -74.010040 40.719971 -74.012268 40.706718 N 429 7.150000 -3.823568 -2.461500 -5.298809 -2.649362 2.098018 1.487155
4 id2181028 2 2016-03-26 13:30:55 2016-03-26 13:38:10 1 -73.973053 40.793209 -73.972923 40.782520 N 435 7.250000 4.329328 0.657515 3.139453 0.668452 2.110213 1.189925 
data_frame.columns
Index(['id', 'vendor_id', 'pickup_datetime', 'dropoff_datetime',
       'passenger_count', 'pickup_longitude', 'pickup_latitude',
       'dropoff_longitude', 'dropoff_latitude', 'store_and_fwd_flag',
       'trip_duration', 'duration [min]', 'src lat [km]', 'src long [km]',
       'dst lat [km]', 'dst long [km]', 'log duration', 'euclidian distance'],
      dtype='object')
import pydeck as pdk
# Define a layer to display on a map
layer = pdk.Layer(
    "HexagonLayer",
    data_frame[:1000],
    get_position=["pickup_longitude", "pickup_latitude"],
    auto_highlight=True,
    elevation_scale=50,
    pickable=True,
    elevation_range=[0, 50],
    extruded=True,
    coverage=1,
)

# Set the viewport location
view_lon = np.mean(data_frame["pickup_longitude"])
view_lat = np.mean(data_frame["pickup_latitude"])

view_state = pdk.ViewState(
    longitude=view_lon, latitude=view_lat, zoom=10, min_zoom=5, max_zoom=15, pitch=40.5, bearing=-27.36,
)

# Render
r = pdk.Deck(layers=[layer], initial_view_state=view_state)
r.show()
#r.to_html("hexagon_ny_taxi.html")
layer = pdk.Layer(
    "HeatmapLayer",
    data_frame[:1000],
    get_position=["pickup_longitude", "pickup_latitude"],
    auto_highlight=True,
    elevation_scale=50,
    pickable=True,
    elevation_range=[0, 50],
    extruded=True,
    coverage=1,
)

# Set the viewport location
view_lon = np.mean(data_frame["pickup_longitude"])
view_lat = np.mean(data_frame["pickup_latitude"])

view_state = pdk.ViewState(
    longitude=view_lon, latitude=view_lat, zoom=10, min_zoom=5, max_zoom=15, pitch=40.5, bearing=-27.36,
)

# Render
r = pdk.Deck(layers=[layer], initial_view_state=view_state)
r.show()
#folium 을 이용해서도 예제로 해보기

Closing in on Manhattan

imageSizeMan = (720,480)
latRangeMan = [-8,10]
longRangeMan = [-5,7]

indToKeep  = np.logical_and(allLat > latRangeMan[0], allLat < latRangeMan[1])
indToKeep  = np.logical_and(indToKeep, np.logical_and(allLong > longRangeMan[0], allLong < longRangeMan[1]))
allLatMan  = allLat[indToKeep]
allLongMan = allLong[indToKeep]

allLatIndsMan  = (imageSizeMan[0]-1) - (imageSizeMan[0] * (allLatMan  - latRangeMan[0])
                                                        / (latRangeMan[1] - latRangeMan[0])).astype(int)
allLongIndsMan =                       (imageSizeMan[1] * (allLongMan - longRangeMan[0])
                                                        / (longRangeMan[1] - longRangeMan[0])).astype(int)

locationDensityImageMan = np.zeros(imageSizeMan)
for latInd, longInd in zip(allLatIndsMan,allLongIndsMan):
    locationDensityImageMan[latInd,longInd] += 1

fig, ax = plt.subplots(nrows=1,ncols=1,figsize=(12,18))
ax.imshow(np.log(locationDensityImageMan+1),cmap='inferno')
ax.set_axis_off()

Cluster the Trips and Look at their distribution

pickupTime = pd.to_datetime(data_frame['pickup_datetime'])

data_frame['src hourOfDay'] = (pickupTime.dt.hour*60.0 + pickupTime.dt.minute)   / 60.0
data_frame['dst hourOfDay'] = data_frame['src hourOfDay'] + data_frame['duration [min]'] / 60.0

data_frame['dayOfWeek']     = pickupTime.dt.weekday
data_frame['hourOfWeek']    = data_frame['dayOfWeek']*24.0 + data_frame['src hourOfDay']

data_frame['monthOfYear']   = pickupTime.dt.month
data_frame['dayOfYear']     = pickupTime.dt.dayofyear
data_frame['weekOfYear']    = pickupTime.dt.weekofyear
data_frame['hourOfYear']    = data_frame['dayOfYear']*24.0 + data_frame['src hourOfDay']
FutureWarning: Series.dt.weekofyear and Series.dt.week have been deprecated.  Please use Series.dt.isocalendar().week instead.
  data_frame['weekOfYear']    = pickupTime.dt.weekofyear
tripAttributes = np.array(data_frame.loc[:,['src lat [km]','src long [km]','dst lat [km]','dst long [km]','duration [min]']])
meanTripAttr = tripAttributes.mean(axis=0)
stdTripAttr  = tripAttributes.std(axis=0)
tripAttributes = stats.zscore(tripAttributes, axis=0)

numClusters = 40
TripKmeansModel = cluster.MiniBatchKMeans(n_clusters=numClusters, batch_size=120000, n_init=100, random_state=1)
clusterInds = TripKmeansModel.fit_predict(tripAttributes)

clusterTotalCounts, _ = np.histogram(clusterInds, bins=numClusters)
sortedClusterInds = np.flipud(np.argsort(clusterTotalCounts))

plt.figure(figsize=(12,4)); plt.title('Cluster Histogram of all trip')
plt.bar(range(1,numClusters+1),clusterTotalCounts[sortedClusterInds])
plt.ylabel('Frequency [counts]'); plt.xlabel('Cluster index (sorted by cluster frequency)')
plt.xlim(0,numClusters+1)
(0.0, 41.0)

Plot typical Trips on the Map

def ConvertToImageCoords(latCoord, longCoord, latRange, longRange, imageSize):
    latInds  = imageSize[0] - (imageSize[0] * (latCoord  - latRange[0])  / (latRange[1]  - latRange[0]) ).astype(int)
    longInds =                (imageSize[1] * (longCoord - longRange[0]) / (longRange[1] - longRange[0])).astype(int)

    return latInds, longInds

templateTrips = TripKmeansModel.cluster_centers_ * np.tile(stdTripAttr,(numClusters,1)) + np.tile(meanTripAttr,(numClusters,1))

srcCoords = templateTrips[:,:2]
dstCoords = templateTrips[:,2:4]

srcImCoords = ConvertToImageCoords(srcCoords[:,0],srcCoords[:,1], latRange, longRange, imageSize)
dstImCoords = ConvertToImageCoords(dstCoords[:,0],dstCoords[:,1], latRange, longRange, imageSize)

plt.figure(figsize=(12,12))
plt.imshow(np.log(locationDensityImage+1),cmap='inferno'); plt.grid('off')
plt.scatter(srcImCoords[1],srcImCoords[0],c='m',s=200,alpha=0.8)
plt.scatter(dstImCoords[1],dstImCoords[0],c='g',s=200,alpha=0.8)

for i in range(len(srcImCoords[0])):
    plt.arrow(srcImCoords[1][i],srcImCoords[0][i], dstImCoords[1][i]-srcImCoords[1][i], dstImCoords[0][i]-srcImCoords[0][i],
              edgecolor='c', facecolor='c', width=0.8,alpha=0.4,head_width=10.0,head_length=10.0,length
SyntaxError: unexpected EOF while parsing (<ipython-input-22-39197d099a2f>, line 22)

Calculate the trip distribution for different hours of the weekday

hoursOfDay = np.sort(data_frame['src hourOfDay'].astype(int).unique())
clusterDistributionHourOfDay_weekday = np.zeros((len(hoursOfDay),numClusters))
for k, hour in enumerate(hoursOfDay):
    slectedInds = (data_frame['src hourOfDay'].astype(int) == hour) & (data_frame['dayOfWeek'] <= 4)
    currDistribution, _ = np.histogram(clusterInds[slectedInds], bins=numClusters)
    clusterDistributionHourOfDay_weekday[k,:] = currDistribution[sortedClusterInds]

fig, ax = plt.subplots(nrows=1,ncols=1,figsize=(12,6))
ax.set_title('Trip Distribution during Weekdays', fontsize=12)
ax.imshow(clusterDistributionHourOfDay_weekday); ax.grid('off')
ax.set_xlabel('Trip Cluster'); ax.set_ylabel('Hour of Day')

Calculate the trip distribution for different hours of the weekend

hoursOfDay = np.sort(data_frame['src hourOfDay'].astype(int).unique())
clusterDistributionHourOfDay_weekend = np.zeros((len(hoursOfDay),numClusters))
for k, hour in enumerate(hoursOfDay):
    slectedInds = (data_frame['src hourOfDay'].astype(int) == hour) & (data_frame['dayOfWeek'] >= 5)
    currDistribution, _ = np.histogram(clusterInds[slectedInds], bins=numClusters)
    clusterDistributionHourOfDay_weekend[k,:] = currDistribution[sortedClusterInds]

fig, ax = plt.subplots(nrows=1,ncols=1,figsize=(12,6))
ax.set_title('Trip Distribution during Weekends', fontsize=12)
ax.imshow(clusterDistributionHourOfDay_weekend); ax.grid('off')
ax.set_xlabel('Trip Cluster'); ax.set_ylabel('Hour of Day')

Calculate the trip distribution for day of week

daysOfWeek = np.sort(data_frame['dayOfWeek'].unique())
clusterDistributionDayOfWeek = np.zeros((len(daysOfWeek),numClusters))
for k, day in enumerate(daysOfWeek):
    slectedInds = data_frame['dayOfWeek'] == day
    currDistribution, _ = np.histogram(clusterInds[slectedInds], bins=numClusters)
    clusterDistributionDayOfWeek[k,:] = currDistribution[sortedClusterInds]

plt.figure(figsize=(12,5)); plt.title('Trip Distribution throughout the Week')
plt.imshow(clusterDistributionDayOfWeek); plt.grid('off')
plt.xlabel('Trip Cluster'); plt.ylabel('Day of Week')

Calculate the trip distribution for day of year

daysOfYear = data_frame['dayOfYear'].unique()
daysOfYear = np.sort(daysOfYear)
clusterDistributionDayOfYear = np.zeros((len(daysOfYear),numClusters))
for k, day in enumerate(daysOfYear):
    slectedInds = data_frame['dayOfYear'] == day
    currDistribution, _ = np.histogram(clusterInds[slectedInds], bins=numClusters)
    clusterDistributionDayOfYear[k,:] = currDistribution[sortedClusterInds]

fig, ax = plt.subplots(nrows=1,ncols=1,figsize=(10,16))
ax.set_title('Trip Distribution throughout the Year', fontsize=12)
ax.imshow(clusterDistributionDayOfYear); ax.grid('off')
ax.set_xlabel('Trip Cluster'); ax.set_ylabel('Day of Year')
ax.annotate('Large Snowstorm', color='r', fontsize=15 ,xy=(5, 21), xytext=(20, 17),
            arrowprops=dict(facecolor='red', shrink=0.03))
ax.annotate('Memorial Day', color='r', fontsize=15, xy=(5, 151), xytext=(20, 157),
            arrowprops=dict(facecolor='red', shrink=0.03))

Computing PCA coefficients

hoursOfYear = np.sort(data_frame['hourOfYear'].astype(int).unique())
clusterDistributionHourOfYear = np.zeros((len(range(hoursOfYear[0],hoursOfYear[-1])),numClusters))
dayOfYearVec  = np.zeros(clusterDistributionHourOfYear.shape[0])
weekdayVec    = np.zeros(clusterDistributionHourOfYear.shape[0])
weekOfYearVec = np.zeros(clusterDistributionHourOfYear.shape[0])
for k, hour in enumerate(hoursOfYear):
    slectedInds = data_frame['hourOfYear'].astype(int) == hour
    currDistribution, _ = np.histogram(clusterInds[slectedInds], bins=numClusters)
    clusterDistributionHourOfYear[k,:] = currDistribution[sortedClusterInds]

    dayOfYearVec[k]  = data_frame[slectedInds]['dayOfYear'].mean()
    weekdayVec[k]    = data_frame[slectedInds]['dayOfWeek'].mean()
    weekOfYearVec[k] = data_frame[slectedInds]['weekOfYear'].mean()

numComponents = 3
TripDistributionPCAModel = decomposition.PCA(n_components=numComponents,whiten=True, random_state=1)
compactClusterDistributionHourOfYear = TripDistributionPCAModel.fit_transform(clusterDistributionHourOfYear)

Collect traces for all weeks of year

listOfFullWeeks = []
for uniqueVal in np.unique(weekOfYearVec):
    if (weekOfYearVec == uniqueVal).sum() == 24*7:
        listOfFullWeeks.append(uniqueVal)

weeklyTraces = np.zeros((24*7,numComponents,len(listOfFullWeeks)))
for k, weekInd in enumerate(listOfFullWeeks):
    weeklyTraces[:,:,k] = compactClusterDistributionHourOfYear[weekOfYearVec == weekInd,:]

fig, axArray = plt.subplots(nrows=numComponents,ncols=1,sharex=True, figsize=(10,10))
fig.suptitle('PCA coefficients during the Week', fontsize=25)
for PC_coeff in range(numComponents):
    meanTrace = weeklyTraces[:,PC_coeff,:].mean(axis=1)
    axArray[PC_coeff].plot(weeklyTraces[:,PC_coeff,:],'red',linewidth=1.5)
    axArray[PC_coeff].plot(meanTrace,'k',linewidth=2.5)
    axArray[PC_coeff].set_ylabel('PC %d coeff' %(PC_coeff+1))
    axArray[PC_coeff].vlines([0,23,47,71,95,119,143,167], weeklyTraces[:,PC_coeff,:].min(), weeklyTraces[:,PC_coeff,:].max(), colors='black', lw=2)

axArray[PC_coeff].set_xlabel('hours since start of week')
axArray[PC_coeff].set_xlim(-0.9,24*7-0.1)

Examine what different PC coefficients mean by looking at their trip template distributions

fig, axArray = plt.subplots(nrows=numComponents,ncols=1,sharex=True, figsize=(12,11))
fig.suptitle('Trip Distribution PCA Components', fontsize=25)
for PC_coeff in range(numComponents):
    tripTemplateDistributionDifference = TripDistributionPCAModel.components_[PC_coeff,:] * \
                                         TripDistributionPCAModel.explained_variance_[PC_coeff]
    axArray[PC_coeff].bar(range(1,numClusters+1),tripTemplateDistributionDifference)
    axArray[PC_coeff].set_title('PCA %d component' %(PC_coeff+1))
    axArray[PC_coeff].set_ylabel('delta frequency [counts]')
    
axArray[PC_coeff].set_xlabel('cluster index (sorted by cluster frequency)')
axArray[PC_coeff].set_xlim(0,numClusters+0.5)

axArray[1].hlines([-25,25], 0, numClusters+0.5, colors='r', lw=0.7)
axArray[2].hlines([-11,11], 0, numClusters+0.5, colors='r', lw=0.7)

We can see that the first PCA component looks very similar to the overall trip distribution, suggesting that it’s mainly a “gain” component that controls just the number of total trips in that period of time.